Suppose you are taking the bus home, and can take either Route 51 or Route 82. You know that the Route 82 will arrive at the bus stop in exactly 5 minutes, but because Route 51 is unreliable, you believe that the amount of time until it arrives is uniformly distributed between 0 and 20 minutes. You take the first bus that arrives. Let T be the number of minutes you wait until you board a bus. Find E[T].

E[T] = 10

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the expected value of the uniform distribution is given by:

Uniformly distributed between 0 and 20 minutes.

This means that

Let T be the number of minutes you wait until you board a bus. Find E[T].

This is

E[T] = 10

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23